Audio signal coding methods of compressing the data amount of a multi-channel audio signal having three or more channels have been developed. As one of such coding methods, the MPEG Surround method standardized by Moving Picture Experts Group (MPEG) is known. Outline of the MPEG Surround method is disclosed, for example, in a MPEG Surround Specification: ISO/IEC23003-1. In the MPEG Surround method, for example, an audio signal of 5.1 channels (5.1 ch) to be encoded is subjected to time-frequency transformation, and a frequency signal thus obtained through time-frequency transformation is downmixed and thereby a three-channel frequency signal is generated once. Further, the three-channel frequency signal is downmixed again to calculate a frequency signal corresponding to a two-channel stereo signal. Then, the frequency signal corresponding to the stereo signal is encoded by the Advanced Audio Coding (MC) coding method, and the Spectral band replication (SBR) coding method. On the other hand, in the MPEG Surround method, when 5.1 channel signal is downmixed to produce a three-channel signal and the three channel signal is downmixed to produce a two channel signal, spatial information representing sound spread or localization is calculated and then encoded. In such a manner, the MPEG Surround method encodes a stereo signal generated by downmixing a multi-channel audio signal and spatial information having relatively less data amount. Thus, the MPEG Surround method provides compression efficiency higher than the efficiency obtained by independently coding signals of channels contained in the multi-channel audio signal.
In the MPEG Surround method, the three-channel frequency signal is encoded by dividing into a stereo frequency signal and two predictive coefficients (channel prediction coefficients) in order to reduce the amount of encoded information. The predictive coefficient is a coefficient for predictively coding a signal of one of three channels based on signals of other two channels. A plurality of predictive coefficients are stored in a table called the codebook, which is used for improving the efficiency of bits to be used. With an encoder and a decoder having a common predetermined codebook (or a codebook prepared in a common way), important information can be sent with less number of bits. When encoding, a predictive coefficient is selected from the codebook. When decoding, a signal of one of three channels is reproduced based on the selected predictive coefficient.